For wideband receivers, such as multi-standard software defined radios (SDR) and multi-standard TV receivers, they usually suffer from harmonic-mixing problem if frequency translation exists, no matter single-conversion (up-conversion or down-conversion), or dual-conversion. The harmonic-mixing problem is basically caused by local oscillator (LO) harmonics and further leads unwanted signals, interferers, or blockers to be translated into the desired channel, along with the desired signal, thus degrading the signal-to-noise ratio.
For example, in a down-conversion case, the mixer is used for translating a signal from a radio frequency fRF to an intermediate frequency fIF based on the multiplication of the input signal at radio frequency fRF with a local oscillation signal at a local oscillation frequency fLO. Since most of the local oscillation signal is in a form of a square-wave type, it includes not only fundamental component at the local oscillation frequency fLO, but also components at harmonics of fLO. Hence, the multiplication will introduce additional spectral components of the input signal that are not at the desired radio frequency fRF, into the intermediate frequency fIF.
Conventional wideband receivers usually demand a high-Q band-pass tracking filter in front of the mixer or LNA to reject all unwanted signals, interferers or blocks, so as to alleviate linearity requirements and prevent from being converted to the desired channel due to harmonic-mixing. Furthermore, the Harmonic-Rejection Mixer (HRM) might be necessary for more stringent standard requirements to enhance 3rd-order and 5th-order harmonic-rejection ratio. In addition, modern CMOS IC design desires to integrate tracking filter on a chip, instead of bulky and high-cost external components, for small size, low cost, and low power consumption considerations. The translational filter has the advantage of high-Q, low-cost, and precisely tunable center frequency and thus can be a good candidate for such an on-chip tracking filter. However, there still exists harmonic-mixing problem for translational filter used in wideband system since it performs frequency translation as well. Moreover, conventional harmonic-rejection techniques can be applied to mixer only (down-conversion or up-conversion one time), but not suitable for translational filter which can be regarded as to perform down-conversion and up-conversion simultaneously. Therefore, there is a need to provide a novel technique to realize a translational filter with the ability of harmonic-rejection for wideband applications.